In order to determine the depth of a three-dimensional scene with no physical contact to the objects; that is, to determine the distance to each of the objects, various techniques have been proposed. Such techniques are roughly classified into twofold: the active technique and the passive technique. The active technique involves irradiating the object with an infrared ray, an ultrasonic wave, and a laser to obtain the distance to the object based either on the time period in which the reflected wave bounces back or on the angle of the reflected wave. The passive technique involves obtaining the distance based on the image of the object. Particularly, in the case where a camera determines the distance to the object, the passive technique is widely used since no devices, such as an infrared emitter, are required.
The passive technique includes a variety of techniques, one of which is called the Depth from Defocus (hereinafter referred to as the DFD). The DFD is to determine distance based on a blur developed by the change of the focus. The features of the DFD are (i) only one camera is required, and (ii) the distance can be determined out of only a few images.
Briefly described hereinafter is how the DFD works.
If a captured image is I (x,y) and an original image with no lens blur is S (x,y), the relationship in an expression (1) holds therebetween:[Math. 1]I(x,y)=S(x,y)*h(x,y,d(x,y))  (1)
Here, h denotes a Point Spread Function (PSF) representing a blur of the camera system, and d (x,y) denotes the distance (hereinafter, referred to as “distance of the object”) from the principal point of the lens at a point (x,y) to the object. Moreover, “*” in the expressions represents a convolution operation.
The expression (1) includes S(x,y) and d(x,y) as unknowns. Captured here is an image I2 (x,y) of the same scene with a shifted focused point. The shift of the focused point is the change of the PSF with respect to the same distance of the object. In other words, the following expression (2) holds:[Math. 2]I2(x,y)=S(x,y)*h′(x,y,d(x,y))  (2)
Here, h′ denotes another PSF which has a focused point different from that of h. By solving the above expressions, the original image of the scene S(x,y) and the distance of the object d(x,y) are obtained. A variety of solutions have been proposed, including Non Patent Literature.
The problem here is that the change of a focused point in a regular camera system causes variation in magnification. The variation in the magnification shifts the position of the original image S(x,y) between the cases where the original image S(x,y) corresponds to the captured image the captured image I(x,y) and where the original image S(x,y) corresponds to the captured image I2(x,y). Such a variation prevents the accurate determination of the distance. In order to solve the above problem, Patent Literatures 1 and 2 disclose techniques to utilize telecentric optical systems.